Surface Reflectance Estimation and Natural Illumination Statistics

Humans recognize optical reflectance properties of surfaces such as metal, plastic, or paper from a single image without knowledge of illumination. We develop a machine vision system to perform similar recognition tasks automatically. Reflectance estimation under unknown, arbitrary illumination proves highly underconstrained due to the variety of potential illumination distributions and surface reflectance properties. We have found that the spatial structure of real-world illumination possesses some of the statistical regularities observed in the natural image statistics literature. A human or computer vision system may be able to exploit this prior information to determine the most likely surface reflectance given an observed image. We develop an algorithm for reflectance classification under unknown real-world illumination, which learns relationships between surface reflectance and certain features (statistics) computed from a single observed image. We also develop an automatic feature selection method.

Surface Reflectance Recognition and Real-World Illumination Statistics

Humans distinguish materials such as metal, plastic, and paper effortlessly at a glance. Traditional computer vision systems cannot solve this problem at all. Recognizing surface reflectance properties from a single photograph is difficult because the observed image depends heavily on the amount of light incident from every direction. A mirrored sphere, for example, produces a different image in every environment. To make matters worse, two surfaces with different reflectance properties could produce identical images. The mirrored sphere simply reflects its surroundings, so in the right artificial setting, it could mimic the appearance of a matte ping-pong ball. Yet, humans possess an intuitive sense of what materials typically "look like" in the real world. This thesis develops computational algorithms with a similar ability to recognize reflectance properties from photographs under unknown, real-world illumination conditions. Real-world illumination is complex, with light typically incident on a surface from every direction. We find, however, that real-world illumination patterns are not arbitrary. They exhibit highly predictable spatial structure, which we describe largely in the wavelet domain. Although they differ in several respects from the typical photographs, illumination patterns share much of the regularity described in the natural image statistics literature. These properties of real-world illumination lead to predictable image statistics for a surface with given reflectance properties. We construct a system that classifies a surface according to its reflectance from a single photograph under unknown illuminination. Our algorithm learns relationships between surface reflectance and certain statistics computed from the observed image. Like the human visual system, we solve the otherwise underconstrained inverse problem of reflectance estimation by taking advantage of the statistical regularity of illumination. For surfaces with homogeneous reflectance properties and known geometry, our system rivals human performance.

Selecting Relevant Genes with a Spectral Approach

Array technologies have made it possible to record simultaneously the expression pattern of thousands of genes. A fundamental problem in the analysis of gene expression data is the identification of highly relevant genes that either discriminate between phenotypic labels or are important with respect to the cellular process studied in the experiment: for example cell cycle or heat shock in yeast experiments, chemical or genetic perturbations of mammalian cell lines, and genes involved in class discovery for human tumors. In this paper we focus on the task of unsupervised gene selection. The problem of selecting a small subset of genes is particularly challenging as the datasets involved are typically characterized by a very small sample size ?? the order of few tens of tissue samples ??d by a very large feature space as the number of genes tend to be in the high thousands. We propose a model independent approach which scores candidate gene selections using spectral properties of the candidate affinity matrix. The algorithm is very straightforward to implement yet contains a number of remarkable properties which guarantee consistent sparse selections. To illustrate the value of our approach we applied our algorithm on five different datasets. The first consists of time course data from four well studied Hematopoietic cell lines (HL-60, Jurkat, NB4, and U937). The other four datasets include three well studied treatment outcomes (large cell lymphoma, childhood medulloblastomas, breast tumors) and one unpublished dataset (lymph status). We compared our approach both with other unsupervised methods (SOM,PCA,GS) and with supervised methods (SNR,RMB,RFE). The results clearly show that our approach considerably outperforms all the other unsupervised approaches in our study, is competitive with supervised methods and in some case even outperforms supervised approaches.